Elements of plane geometry, book i, containing nearly the same propositions as the first book of Euclid's Elements1865 |
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Resultat 1-5 av 12
Side 43
... angle A is ... angle B to DEF , and C to DFE , the equal angles being always opposite to the equal sides . PROPOSITION XII . THEOR . If two triangles have two sides , and the included angle of the one equal to two sides , and the included ...
... angle A is ... angle B to DEF , and C to DFE , the equal angles being always opposite to the equal sides . PROPOSITION XII . THEOR . If two triangles have two sides , and the included angle of the one equal to two sides , and the included ...
Side 45
... angle B is also equal to the angle C. Bisect the angle BAC ( 13 ) by the straight line AD , then , in the two triangles ABD and ACD , the side AB is equal to the side AC ; the side AD is common to both , and the included angles BAD and ...
... angle B is also equal to the angle C. Bisect the angle BAC ( 13 ) by the straight line AD , then , in the two triangles ABD and ACD , the side AB is equal to the side AC ; the side AD is common to both , and the included angles BAD and ...
Side 46
... angle is greater than either of the interior opposite angles . Let ABC be a ... included angles AEB and CEF are equal , because ( 7 ) they are verti- B cal ... angles ABC , ACB , are together less than 46 ELEMENTS OF PLANE GEOMETRY .
... angle is greater than either of the interior opposite angles . Let ABC be a ... included angles AEB and CEF are equal , because ( 7 ) they are verti- B cal ... angles ABC , ACB , are together less than 46 ELEMENTS OF PLANE GEOMETRY .
Side 50
... included angle ACE is equal to the included angle BCE ; therefore ( 12 ) AE is equal to BE . Again , any point F that is not in the perpendicular is A C B unequally distant from A and B. Draw AF , cutting CD in G , and join FB and GB ...
... included angle ACE is equal to the included angle BCE ; therefore ( 12 ) AE is equal to BE . Again , any point F that is not in the perpendicular is A C B unequally distant from A and B. Draw AF , cutting CD in G , and join FB and GB ...
Side 51
... angle ; hence CE is less than CF. AF E D G B Make ( 2 ) DG equal to DE , and join CG . In the triangles CDE and CDG , the side ED is equal to DG , and CD is common to both , and the included angles at D are equal ; therefore ( 12 ) the ...
... angle ; hence CE is less than CF. AF E D G B Make ( 2 ) DG equal to DE , and join CG . In the triangles CDE and CDG , the side ED is equal to DG , and CD is common to both , and the included angles at D are equal ; therefore ( 12 ) the ...
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Elements of Plane Geometry, Book: Containing Nearly the Same Propositions As ... Euclid Ingen forhåndsvisning tilgjengelig - 2008 |
Vanlige uttrykk og setninger
AB is equal ABC and DEF ABC is equal acute adjacent angles ancient geometers angle ACD angle AGH angle BAC angles ABC angles equal angular magnitude base BC bisect centre circumference coincide diagonal drawn EBCF equal alternate angles equal Def equal to BC Euclid EUCLID'S ELEMENTS exterior angle figure has sides four right angles geometers given point given straight line greater than AC included angle interior opposite angle intersect isosceles triangle join less Let ABC Let the straight method method of exhaustions parallel lines parallel to CD parallelogram ABCD perpendicular PLANE GEOMETRY point F PROB proof properties of parallel PROPOSITION Pythagoras radius rectangle rectilineal figure reductio ad absurdum Scholium side AB side AC straight line BC THEOR theorem three angles three sides triangle ABC triangle DEF triangles are equal truths unequal vertex vertical angle wherefore
Populære avsnitt
Side 43 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal.
Side 46 - Any two angles of a triangle are together less than two right angles.
Side 37 - The angles which one straight line makes with another upon one tide of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.
Side 57 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Side 38 - ... in one and the same straight line. At the point B in the straight line AB, let the two straight lines BC, BD upon the opposite sides of AB, make the adjacent angles ABC, ABD, equal together to two right angles. BD is in the same straight line with CB.
Side 68 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 34 - LET it be granted that a straight line may be drawn from any one point to any other point.
Side 64 - Parallelograms upon the same base, and between the same parallels, are equal to one another.
Side 46 - If one side of a triangle be produced, the exterior angle is greater than either of the interior, and opposite angles.
Side 34 - Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal.